Traditional MRI can provide several advantages compared to other imaging modalities (e.g., computed tomography (“CT”)), such as a superior soft-tissue characterization, absence of an ionizing radiation and flexible image contrast, etc. However, conventional MRI techniques can be relatively slow, which can limit temporal and spatial resolution and volumetric coverage, and can introduce motion related artifacts. In MRI, the imaging data can be commonly acquired as samples of the Fourier transform of the object to be reconstructed (e.g., a spatial distributed set of NMR signal sources that can evolve in time). The image reconstruction process can involve recovering an estimate (e.g., an image) of the original object from these samples. As only a limited number of these samples of the Fourier transform (e.g., “k-space”) can be acquired at a time, with a delay between each such data set acquired imposed by the signal excitation and encoding process, the total time for data acquisition can be dependent on the spatial and temporal image resolution desired, and the size of the object. 3D image data can similarly be more time-consuming than 2D imaging. In order to reduce the image acquisition time (e.g., in order to more accurately capture moving objects, such as the heart, or to minimize the risk of patient motion during the data acquisition, which can lead to artifacts, or simply to reduce the total time for the MRI examination), more efficient ways of accurately reconstructing the image from a reduced number of k-space samples can be needed.
Some recent methods for reducing the amount of k-space sampling for image reconstruction can include: a) radial sampling of k-space without loss of generality, (the orientations of these radial samples can be designated as lying in the kx-ky plane, which can be more robust to undersampling by presenting low-value streaking aliasing artifacts in the reconstructed image, distributed over the complete field of view); b) spiral sampling of k-space, which can acquire more samples per acquisition which can have similar benefits to radial sampling in reconstruction of radial sampling, and which can be considered as a special case of spiral sampling); c) golden-angle ordering of the acquisition of the radial sets of samples, which can help to maintain a fairly uniform distribution of sampling locations while different amounts of radial k-space data can be acquired; and d) using compressed sensing or sampling (“CS”) approaches to image reconstruction, which can rely on the compressibility of the final images to reduce the amount of imaging k-space data to be acquired, at the cost of increased computational effort in the image reconstruction process.
There has been prior work on producing faster 3D MRI by combining 2D radial sampling with the use of golden-angle ordering for the sequence of the radial sample acquisitions, with a regularly spaced set of samples acquired in the remaining (e.g., “kz”) direction, thus producing a “stack of stars” sampling pattern in k-space (FIG. 1E). This approach to 3D MRI can be further accelerated by combining it with CS image reconstruction methods, thus enabling equivalent quality image reconstruction from a sparser, and more rapidly acquired, set of k-space samples (See e.g., References 16 and 19). This can also provide increased flexibility in trading off relative optimization of the imaging time and the effective temporal resolution and sampling density of the final images during the image reconstruction, which can be valuable for dynamic imaging.
CS procedures (See, e.g., References 1-3) can provide a rapid imaging approach, exploiting image sparsity and compressibility. Instead of acquiring a fully-sampled image and compressing it afterwards (e.g., standard compression), CS takes advantage of the fact than an image can usually be sparse in some appropriate basis, and can reconstruct this sparse representation from undersampled data, for example, without loss of important information. Successful applications of CS generally use image sparsity and incoherent measurements. MRI can provide these two basic preferences, since (a) medical images can naturally be compressible by using appropriate sparsifying transforms, such as wavelets, finite differences, principal component analysis (“PCA”) and other techniques, and (b) MRI data can be acquired in the spatial frequency domain (e.g., k-space) rather than in the image domain, which can facilitate the generation of incoherent aliasing artifacts. Moreover, CS can be combined with previous acceleration methods in MRI, such as parallel imaging, to further increase the imaging speed.
Parallel imaging can be a traditional acceleration technique in MRI that can employ multiple receiver coils with different spatial sensitivities to reconstruct images from regularly undersampled k-space data. Combinations of CS and parallel imaging have been provided in several variants, for example using the notion of joint multicoil sparsity, where sparsity can be enforced on the signal ensemble from multiple receiver coils rather than on each coil separately (See, e.g., References 4-8).
Dynamic MRI can be used for CS, due to (a) extensive correlations between image frames which can typically result in sparse representations after applying an appropriate temporal transform, such as FFT, PCA or finite differences, which can be equivalent to total variation (“TV”) minimization, and (b) the possibility of using a different random undersampling pattern for each temporal frame, which can increase incoherence, and can distribute the incoherent aliasing artifacts along the temporal dimension which can result in artifacts with lower intensity (See, e.g., References 8-10).
Significant amount of current work on CS MRI uses random undersampling of Cartesian k-space trajectories to increase data acquisition speed. However, in Cartesian trajectories, it can be possible that only undersampling of phase-encoding dimensions (e.g., y and z) can account for faster imaging, which can limit the performance of compressed sensing, since incoherence and sparsity along the other spatial dimension (e.g., x) cannot be exploited. Radial k-space sampling can provide an attractive alternative for compressed sensing MRI, due to the inherent presence of incoherent aliasing artifacts along all spatial dimensions, even for regular undersampling. Although the readout dimension can also be fully-sampled in radial MRI, the situation can be different from Cartesian MRI, since skipping radial lines can effectively undersample all spatial dimensions, which can distribute the overall acceleration along these dimensions and can result in lower aliasing artifacts.
Radial trajectories can be less sensitive to motion, which can facilitate a better performance in capturing dynamic information. FIGS. 1A-1D show illustrations associated with a highly increased incoherence of radial sampling compared to Cartesian sampling for static and dynamic imaging, which can be due to the inherent presence of low-value streaking aliasing artifacts that can spread out along all spatial dimensions in radial sampling. For example, FIGS. 1A-1D illustrate a k-space sampling patterns, point spread functions (“PSFs”) and incoherence of Cartesian and radial trajectories with 12.8-fold acceleration for static and dynamic imaging. The PSFs can be computed by applying an inverse Fourier transform to the k-space sampling mask, where the sampled positions can be equal to 1, and the non-sampled positions can be equal to 0. The standard deviation of the PSF side lobes can be used to quantify the power of the resulting incoherent artifacts (e.g., pseudo-noise). Incoherences can be computed using the main-lobe to pseudo-noise ratio of the PSF (See, e.g., References 3). The PSFs for dynamic imaging can be computed in the space of temporal frequencies, after a temporal FFT, which can be usually employed to sparsify dynamic MRI data. Compressed sensing radial MRI using regular undersampling of radial trajectories has been previously described and successfully applied to cardiac perfusion (See, e.g., Reference 11), cardiac cine (See, e.g., Reference 12), and breast MRI (See, e.g., Reference 13). However, even though these studies can use coil arrays, only coil-by-coil reconstructions can be performed, which can limit the performance. Furthermore, the acquisition trajectory can be limited to skipping a specific number of radial lines, which can present only a limited gain in incoherence. Other radial MRI techniques can lead to better performance in CS. For example, the golden-angle acquisition procedure (See, e.g., Reference 14) can be utilized, where radial lines can be continuously acquired with an angular increment of 111.25°, such that each line can provide complementary information. Uniform coverage of k-space can be accomplished by grouping a specific number of consecutive radial lines, which can lead to improved temporal incoherence. Moreover, golden-angle radial acquisition can enable continuous data acquisition and reconstruction with arbitrary temporal resolution by grouping a different number of consecutive radial lines to form each temporal frame.
In dynamic imaging procedures, where a time-series of images can be acquired to visualize organ function or to follow the passage of a contrast agent, spatial resolution and volumetric coverage can usually be sacrificed in order to maintain an adequate temporal resolution and reduce motion-related artifacts.
Respiratory motion can degrade image quality, and reduce the performance of compressed sensing (See e.g., Reference 15) since temporal sparsity can be decreased. To minimize the effects of respiratory motion, MRI data acquisition can be performed during breath-holds, or using navigator or respiratory-bellow gating. However, breath-holds can be subject dependent, with limited duration in patients, and the use of navigator or respiratory-bellow gating can utilize long acquisition times to acquire data during an interval of moderate respiratory motion. Non-Cartesian imaging procedures can offer self-gating by estimating the respiratory-motion signal from the oversampled k-space center. However, current gating techniques can be inefficient since they only use the data acquired during an interval of moderate respiratory motion (e.g., expiration) and discard the rest, which can correspond to a large percentage of the total amount of acquired data.
Thus, it may be beneficial to provide an exemplary imaging apparatus that can combine carious CS, golden-angle, and parallel imaging procedures to decrease the image acquisition time, while maintaining a high level of image quality, and which can overcome at least some of the deficiencies described herein above.